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Each of the four sides of the 100-story John Hancock Center in Chicago Iiinois is shaped like a trapezoid. The highest of the building is 28 feet less than 7 times the length of the base along Michigan. The length of the roof is 65 feet shorter than the length of the base below it. The area of one particular side is 149,327.5 square feet. How long is the base of that side? How tall is the biulding?

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thaovtp1407

Answer:

1227 feet

Step-by-step explanation:

Let x is the the length of the base along Michigan

Given:

  • The highest of the building is 28 feet less than 7 times the length of the base along Michigan

<=> The highest of the building = 7x -28

  • The length of the roof is 65 feet shorter than the length of the base below it.

<=> The length of the roof = x - 65

  • The area of one particular side is 149,327.5 square feet

<=> [tex]\frac{x+ x -65 }{2}[/tex] *(7x -28 ) = 149327.5

<=> (2x -65) (7x -28) = 298655

<=> [tex]14^{2}[/tex] - 511x = 296835

<=> x = 165.

So the building's height is: 7(165) -28  = 1227 feet

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